jqGrid add multi select column filter to a specific column

From your other questions one can see that you use free jqGrid fork. It supports generating of unique values automatically. Thus one can use

searchoptions: {
    generateValue: true,
    sopt: ["in"],
    attr: { multiple: "multiple", size: 7 },
    dataInit: dataInitMultiselect
}

instead of

searchoptions: {
    clearSearch: false,
    sopt: ['eq', 'ne'],
    value: buildSearchSelect(getUniqueNames(columnName, data,grid)),
    attr: { multiple: 'multiple', size: 7},
    dataInit: dataInitMultiselect
}

It's important that unique values of data in the column will be filled only after loading the data. Then one should create or recreate filterToolbar after loading the data from the server. One can test this.ftoolbar inside of loadComplete for example to detect whether filterToolbar already exist:

loadComplete: function () {
    if (!this.ftoolbar) {
        // create filter toolbar if it isn't exist 
        $(this).jqGrid("filterToolbar", {
            defaultSearch: "cn",
            beforeClear: function() {
                $(this.grid.hDiv)
                    .find(".ui-search-toolbar button.ui-multiselect")
                    .each(function() {
                    $(this).prev("select[multiple]").multiselect("refresh");
                });
            }
        });
        $(this).triggerHandler("jqGridRefreshFilterValues");
        $(this.grid.hDiv)
            .find(".ui-search-toolbar button.ui-multiselect")
            .each(function() {
            $(this).prev("select[multiple]")
                .multiselect("refresh");
        });        
    }
}

The demo https://jsfiddle.net/OlegKi/ty4e68pm/2/ shows a possible implementation of usage multiselect in free jqGrid. The function dataInitMultiselect has the following implementation:

var dataInitMultiselect = function (elem, searchOptions) {
        var $grid = $(this);
        setTimeout(function() {
            var $elem = $(elem),
                id = elem.id,
                inToolbar = searchOptions.mode === "filter",
                options = {
                    selectedList: 2,
                    height: "auto",
                    checkAllText: "all",
                    uncheckAllText: "no",
                    noneSelectedText: "Any",
                    open: function() {
                        var $menu = $(".ui-multiselect-menu:visible");
                        $menu.width("auto");
                    }
                },
                $options = $elem.find("option");
            if ($options.length > 0 && $options[0].selected) {
                $options[0].selected = false; // unselect the first selected option

            }
            if (inToolbar) {
                options.minWidth = "auto";
            }
            $grid.triggerHandler("jqGridRefreshFilterValues");
            $elem.multiselect(options);
            // replace icons ui-icon-check, ui-icon-closethick, ui-icon-circle-close
            // and ui-icon-triangle-1-s to font awesome icons
            var $header = $elem.data("echMultiselect").header;
            $header.find("span.ui-icon.ui-icon-check")
                .removeClass("ui-icon ui-icon-check")
                .addClass("fa fa-fw fa-check");
            $header.find("span.ui-icon.ui-icon-closethick")
                .removeClass("ui-icon ui-icon-closethick")
                .addClass("fa fa-fw fa-times");
            $header.find("span.ui-icon.ui-icon-circle-close")
                .removeClass("ui-icon ui-icon-circle-close")
                .addClass("fa fa-times-circle");
            $elem.data("echMultiselect")
                .button
                .find("span.ui-icon.ui-icon-triangle-1-s")
                .removeClass("ui-icon ui-icon-triangle-1-s")
                .addClass("fa fa-caret-down")
                .css({
                    float: "right",
                    marginRight: "5px"
                });

            $elem.siblings("button.ui-multiselect").css({
                width: "100%",
                margin: "1px 0",
                paddingTop: ".3em",
                paddingBottom: ".3em"
            });
        }, 50);
    };

UPDATED: I analysed your demo https://jsfiddle.net/B_AV_B/7ecrmtz4/5/. It contains a lot of error:

  1. you missing stype : "select" in multiselect column. The searching field have to have select type (stype : "select") to be able to be displayed as <select> alement, which can be converted later with respect of multiselect control
  2. I wrote you multiple times about importance inserting only one version of jQuery and other JavaScript libraries. Moreover, it's important to hold the order of inserted JS files based on dependencies. Multiselect widget is plugin to jQuery UI. Thus jQuery UI must be inserted before. In short you should replace
<script src="https://code.jquery.com/jquery-3.3.1.slim.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery-ui-multiselect-widget/2.0.2/jquery.multiselect.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>   

to

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery-ui-multiselect-widget/2.0.2/jquery.multiselect.js"></script>
  1. You should remove ../bootstrap-multiselect/0.9.13/js/bootstrap-multiselect.js, which overwrite multiselect registered previously.
  2. JavaScript is case sensitive. It seems that ID property of input data specifies unique id of every input item. jqGrid uses id instead of ID by default. If you use datatype: "local" then you should include localReader: { id: "ID" } parameter. If you use datatype: "json" then you should include jsonReader: { id: "ID" }. In your case you can include both parameters.
  3. You used wrong code of open callback (compare your code, with the code from my answer). It's enough to use it as var $menu = $(".ui-multiselect-menu:visible"); $menu.width("auto"); without additional actions, which makes some other items invisible.
  4. Values of width property on colModel should be numbers and not strings like "120%". Numbers will be interpreted as pixels. If you use autowidth : true the initial width values will be proportionally increased to make the width of the grid equal to the width of outer element.
  5. Finally I added some CSS rules to your demo
.ui-multiselect-menu .ui-multiselect-header ul,
.ui-multiselect-menu .ui-multiselect-checkboxes li {
    font-size: 12px;
}

.ui-multiselect-menu .ui-multiselect-header a:hover {
    text-decoration: none;
}
.ui-multiselect-menu .ui-multiselect-close {
    margin-right: 3px;
}

You can modify the font-size on the above rule corresponds to your requirements.

Modified demo is https://jsfiddle.net/OlegKi/teLja6z3/25/